1. Fields of the Invention
The present invention relates to an operation circuit and an operation method thereof, especially to operation circuit and an operation method thereof applied to an Ensemble Empirical Mode Decomposition (EEMD) and reducing computation for matrices within a time unit.
2. Descriptions of Related Art
Refer to U.S. Pat. No. 5,983,162 “Computer implemented empirical mode decomposition method, apparatus and article of manufacture”, U.S. Pat. No. 6,311,130 “Computer implemented empirical mode decomposition method, apparatus, and article of manufacture for two-dimensional signals”, U.S. Pat. No. 6,381,559 “Empirical mode decomposition apparatus, method and article of manufacture for analyzing biological signals and performing curve fitting”, U.S. Pat. No. 6,738,734 “Empirical mode decomposition apparatus, method and article of manufacture for analyzing biological signals and performing curve fitting” of National Aeronautics and Space Administration (NASA), and US Pub. App. No. 2008/0065337 “Noise-Assisted Data Analysis Method, System and Program Product Therefore”, the Hilbert-Huang transform (HHT) is the result of the empirical mode decomposition (EMD) and the Hilbert spectral analysis (HSA) and the HHT provides a new time-frequency analytic method to get frequency variation with time.
As early as in 1940s, Gabor used Hilbert transform has been used broadly in signal processing field. Yet while being applied to define the instantaneous frequency of a signal, the Hilbert transform has many shortcomings (Bedrosian 1963, Nuttall 1966). The most serious one is that the derived instantaneous frequency of a signal would lose its physical meaning when the signal is not a mono-component or AM/FM separable oscillatory function (Huang et al. 1998). Thus Dr. Huang proposed Hilbert Huang transform that combines EMD with Hilbert transform to overcome the shortcoming. After being improved, the EMD method has become a powerful tool in signal processing and data analysis and has been applied to various research including climate cycle, earthquake engineering, engineering geophysical exploration, submarine design, damage detection in structures, satellite data analysis, blood pressure changes, cardiac arrhythmias, etc.
Different from all previous decomposition methods, the empirical mode decomposition (EMD) method is experiential, instinctive, Direct, and adaptive, without preset basis functions. The decomposition way can obtain various simple intrinsic modes of oscillation signals according to each data within local time scale. A simple oscillatory mode called intrinsic mode function (IMF) satisfies the following conditions. (a) In the whole data set, there are the same number (or at most differing by one) of extrema and zero crossings. (b) At any time point, the mean value of the upper envelop defined by the local maxima and the envelope defined by the local minima is zero. In short word, the EMD is an adaptive method that decompose data x(t) in terms of IMFs cj and a residual component m. That means in the equation, the residual component m could be a constant, a monotonic function, or a function containing only a single extrema, from which no more IMF can be extracted. Therefore, the decomposition method is adaptive and highly efficient. As the composition method is based on the local characteristics of the data, it is applicable to nonlinear and nonstationary processes.
However, no matter how much improvements have been made in EEMD, its operations are required to be run in the computer system. While being applied to various fields, the operations of EEMD still require the computer system. This causes inconvenience to users.
Thus there is a need to provide an operation circuit applied to EEMD that reduces computation for matrices within a time unit by simplification of matrix operations.